Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,2,Mod(1084,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1805.1084");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.4129975648\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1084.9 | ||
Character | \(\chi\) | \(=\) | 1805.1084 |
Dual form | 1805.2.b.l.1084.16 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times\).
\(n\) | \(362\) | \(1446\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.04740i | − | 0.740625i | −0.928907 | − | 0.370313i | \(-0.879251\pi\) | ||
0.928907 | − | 0.370313i | \(-0.120749\pi\) | |||||||
\(3\) | − | 0.531453i | − | 0.306835i | −0.988161 | − | 0.153417i | \(-0.950972\pi\) | ||
0.988161 | − | 0.153417i | \(-0.0490279\pi\) | |||||||
\(4\) | 0.902948 | 0.451474 | ||||||||
\(5\) | 1.65192 | + | 1.50704i | 0.738762 | + | 0.673967i | ||||
\(6\) | −0.556645 | −0.227250 | ||||||||
\(7\) | 2.74033i | 1.03575i | 0.855457 | + | 0.517874i | \(0.173276\pi\) | ||||
−0.855457 | + | 0.517874i | \(0.826724\pi\) | |||||||
\(8\) | − | 3.04056i | − | 1.07500i | ||||||
\(9\) | 2.71756 | 0.905853 | ||||||||
\(10\) | 1.57847 | − | 1.73023i | 0.499157 | − | 0.547146i | ||||
\(11\) | 0.832835 | 0.251109 | 0.125555 | − | 0.992087i | \(-0.459929\pi\) | ||||
0.125555 | + | 0.992087i | \(0.459929\pi\) | |||||||
\(12\) | − | 0.479874i | − | 0.138528i | ||||||
\(13\) | − | 0.610831i | − | 0.169414i | −0.996406 | − | 0.0847071i | \(-0.973005\pi\) | ||
0.996406 | − | 0.0847071i | \(-0.0269954\pi\) | |||||||
\(14\) | 2.87023 | 0.767101 | ||||||||
\(15\) | 0.800919 | − | 0.877919i | 0.206796 | − | 0.226678i | ||||
\(16\) | −1.37879 | −0.344697 | ||||||||
\(17\) | − | 4.83841i | − | 1.17349i | −0.809773 | − | 0.586744i | \(-0.800410\pi\) | ||
0.809773 | − | 0.586744i | \(-0.199590\pi\) | |||||||
\(18\) | − | 2.84638i | − | 0.670897i | ||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 1.49160 | + | 1.36077i | 0.333532 | + | 0.304278i | ||||
\(21\) | 1.45636 | 0.317803 | ||||||||
\(22\) | − | 0.872314i | − | 0.185978i | ||||||
\(23\) | 3.75094i | 0.782124i | 0.920364 | + | 0.391062i | \(0.127892\pi\) | ||||
−0.920364 | + | 0.391062i | \(0.872108\pi\) | |||||||
\(24\) | −1.61591 | −0.329847 | ||||||||
\(25\) | 0.457688 | + | 4.97901i | 0.0915377 | + | 0.995802i | ||||
\(26\) | −0.639786 | −0.125472 | ||||||||
\(27\) | − | 3.03861i | − | 0.584781i | ||||||
\(28\) | 2.47437i | 0.467613i | ||||||||
\(29\) | −3.97516 | −0.738168 | −0.369084 | − | 0.929396i | \(-0.620329\pi\) | ||||
−0.369084 | + | 0.929396i | \(0.620329\pi\) | |||||||
\(30\) | −0.919534 | − | 0.838884i | −0.167883 | − | 0.153159i | ||||
\(31\) | 6.92676 | 1.24408 | 0.622042 | − | 0.782984i | \(-0.286303\pi\) | ||||
0.622042 | + | 0.782984i | \(0.286303\pi\) | |||||||
\(32\) | − | 4.63696i | − | 0.819707i | ||||||
\(33\) | − | 0.442613i | − | 0.0770490i | ||||||
\(34\) | −5.06777 | −0.869115 | ||||||||
\(35\) | −4.12977 | + | 4.52681i | −0.698059 | + | 0.765170i | ||||
\(36\) | 2.45381 | 0.408969 | ||||||||
\(37\) | 4.33071i | 0.711965i | 0.934493 | + | 0.355982i | \(0.115854\pi\) | ||||
−0.934493 | + | 0.355982i | \(0.884146\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.324628 | −0.0519821 | ||||||||
\(40\) | 4.58222 | − | 5.02276i | 0.724513 | − | 0.794168i | ||||
\(41\) | −5.31691 | −0.830361 | −0.415181 | − | 0.909739i | \(-0.636282\pi\) | ||||
−0.415181 | + | 0.909739i | \(0.636282\pi\) | |||||||
\(42\) | − | 1.52539i | − | 0.235373i | ||||||
\(43\) | − | 10.4585i | − | 1.59490i | −0.603385 | − | 0.797450i | \(-0.706182\pi\) | ||
0.603385 | − | 0.797450i | \(-0.293818\pi\) | |||||||
\(44\) | 0.752007 | 0.113369 | ||||||||
\(45\) | 4.48919 | + | 4.09546i | 0.669209 | + | 0.610514i | ||||
\(46\) | 3.92874 | 0.579261 | ||||||||
\(47\) | − | 3.40016i | − | 0.495965i | −0.968765 | − | 0.247982i | \(-0.920232\pi\) | ||
0.968765 | − | 0.247982i | \(-0.0797675\pi\) | |||||||
\(48\) | 0.732762i | 0.105765i | ||||||||
\(49\) | −0.509407 | −0.0727725 | ||||||||
\(50\) | 5.21503 | − | 0.479384i | 0.737516 | − | 0.0677951i | ||||
\(51\) | −2.57139 | −0.360066 | ||||||||
\(52\) | − | 0.551549i | − | 0.0764861i | ||||||
\(53\) | 13.6679i | 1.87743i | 0.344692 | + | 0.938716i | \(0.387983\pi\) | ||||
−0.344692 | + | 0.938716i | \(0.612017\pi\) | |||||||
\(54\) | −3.18265 | −0.433104 | ||||||||
\(55\) | 1.37578 | + | 1.25511i | 0.185510 | + | 0.169239i | ||||
\(56\) | 8.33212 | 1.11343 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.16359i | 0.546706i | ||||||||
\(59\) | 10.0173 | 1.30414 | 0.652068 | − | 0.758160i | \(-0.273902\pi\) | ||||
0.652068 | + | 0.758160i | \(0.273902\pi\) | |||||||
\(60\) | 0.723188 | − | 0.792715i | 0.0933631 | − | 0.102339i | ||||
\(61\) | 9.07245 | 1.16161 | 0.580804 | − | 0.814043i | \(-0.302738\pi\) | ||||
0.580804 | + | 0.814043i | \(0.302738\pi\) | |||||||
\(62\) | − | 7.25511i | − | 0.921400i | ||||||
\(63\) | 7.44700i | 0.938234i | ||||||||
\(64\) | −7.61435 | −0.951793 | ||||||||
\(65\) | 0.920544 | − | 1.00905i | 0.114179 | − | 0.125157i | ||||
\(66\) | −0.463594 | −0.0570645 | ||||||||
\(67\) | 10.9346i | 1.33587i | 0.744220 | + | 0.667935i | \(0.232821\pi\) | ||||
−0.744220 | + | 0.667935i | \(0.767179\pi\) | |||||||
\(68\) | − | 4.36883i | − | 0.529799i | ||||||
\(69\) | 1.99345 | 0.239983 | ||||||||
\(70\) | 4.74139 | + | 4.32554i | 0.566705 | + | 0.517000i | ||||
\(71\) | 0.677726 | 0.0804313 | 0.0402157 | − | 0.999191i | \(-0.487196\pi\) | ||||
0.0402157 | + | 0.999191i | \(0.487196\pi\) | |||||||
\(72\) | − | 8.26288i | − | 0.973790i | ||||||
\(73\) | 7.01343i | 0.820859i | 0.911892 | + | 0.410430i | \(0.134621\pi\) | ||||
−0.911892 | + | 0.410430i | \(0.865379\pi\) | |||||||
\(74\) | 4.53600 | 0.527299 | ||||||||
\(75\) | 2.64611 | − | 0.243240i | 0.305546 | − | 0.0280869i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.28224i | 0.260086i | ||||||||
\(78\) | 0.340016i | 0.0384993i | ||||||||
\(79\) | 3.47957 | 0.391482 | 0.195741 | − | 0.980656i | \(-0.437289\pi\) | ||||
0.195741 | + | 0.980656i | \(0.437289\pi\) | |||||||
\(80\) | −2.27765 | − | 2.07788i | −0.254649 | − | 0.232315i | ||||
\(81\) | 6.53779 | 0.726421 | ||||||||
\(82\) | 5.56894i | 0.614987i | ||||||||
\(83\) | − | 4.97485i | − | 0.546060i | −0.962005 | − | 0.273030i | \(-0.911974\pi\) | ||
0.962005 | − | 0.273030i | \(-0.0880259\pi\) | |||||||
\(84\) | 1.31501 | 0.143480 | ||||||||
\(85\) | 7.29166 | − | 7.99268i | 0.790891 | − | 0.866927i | ||||
\(86\) | −10.9542 | −1.18122 | ||||||||
\(87\) | 2.11261i | 0.226495i | ||||||||
\(88\) | − | 2.53228i | − | 0.269942i | ||||||
\(89\) | −5.88868 | −0.624198 | −0.312099 | − | 0.950050i | \(-0.601032\pi\) | ||||
−0.312099 | + | 0.950050i | \(0.601032\pi\) | |||||||
\(90\) | 4.28959 | − | 4.70199i | 0.452163 | − | 0.495633i | ||||
\(91\) | 1.67388 | 0.175470 | ||||||||
\(92\) | 3.38690i | 0.353109i | ||||||||
\(93\) | − | 3.68125i | − | 0.381728i | ||||||
\(94\) | −3.56134 | −0.367324 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.46433 | −0.251514 | ||||||||
\(97\) | − | 12.4387i | − | 1.26296i | −0.775391 | − | 0.631482i | \(-0.782447\pi\) | ||
0.775391 | − | 0.631482i | \(-0.217553\pi\) | |||||||
\(98\) | 0.533555i | 0.0538972i | ||||||||
\(99\) | 2.26328 | 0.227468 | ||||||||
\(100\) | 0.413269 | + | 4.49578i | 0.0413269 | + | 0.449578i | ||||
\(101\) | −17.7372 | −1.76492 | −0.882460 | − | 0.470387i | \(-0.844114\pi\) | ||||
−0.882460 | + | 0.470387i | \(0.844114\pi\) | |||||||
\(102\) | 2.69328i | 0.266674i | ||||||||
\(103\) | 5.21849i | 0.514193i | 0.966386 | + | 0.257097i | \(0.0827659\pi\) | ||||
−0.966386 | + | 0.257097i | \(0.917234\pi\) | |||||||
\(104\) | −1.85727 | −0.182120 | ||||||||
\(105\) | 2.40579 | + | 2.19478i | 0.234781 | + | 0.214189i | ||||
\(106\) | 14.3158 | 1.39047 | ||||||||
\(107\) | − | 15.1871i | − | 1.46819i | −0.679044 | − | 0.734097i | \(-0.737606\pi\) | ||
0.679044 | − | 0.734097i | \(-0.262394\pi\) | |||||||
\(108\) | − | 2.74371i | − | 0.264014i | ||||||
\(109\) | 3.92257 | 0.375714 | 0.187857 | − | 0.982196i | \(-0.439846\pi\) | ||||
0.187857 | + | 0.982196i | \(0.439846\pi\) | |||||||
\(110\) | 1.31461 | − | 1.44099i | 0.125343 | − | 0.137393i | ||||
\(111\) | 2.30157 | 0.218455 | ||||||||
\(112\) | − | 3.77834i | − | 0.357019i | ||||||
\(113\) | − | 3.97342i | − | 0.373788i | −0.982380 | − | 0.186894i | \(-0.940158\pi\) | ||
0.982380 | − | 0.186894i | \(-0.0598421\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.65279 | + | 6.19625i | −0.527126 | + | 0.577803i | ||||
\(116\) | −3.58936 | −0.333264 | ||||||||
\(117\) | − | 1.65997i | − | 0.153464i | ||||||
\(118\) | − | 10.4921i | − | 0.965877i | ||||||
\(119\) | 13.2588 | 1.21544 | ||||||||
\(120\) | −2.66936 | − | 2.43524i | −0.243678 | − | 0.222306i | ||||
\(121\) | −10.3064 | −0.936944 | ||||||||
\(122\) | − | 9.50251i | − | 0.860317i | ||||||
\(123\) | 2.82569i | 0.254784i | ||||||||
\(124\) | 6.25451 | 0.561671 | ||||||||
\(125\) | −6.74748 | + | 8.91468i | −0.603513 | + | 0.797353i | ||||
\(126\) | 7.80001 | 0.694880 | ||||||||
\(127\) | 9.18497i | 0.815034i | 0.913198 | + | 0.407517i | \(0.133605\pi\) | ||||
−0.913198 | + | 0.407517i | \(0.866395\pi\) | |||||||
\(128\) | − | 1.29864i | − | 0.114785i | ||||||
\(129\) | −5.55818 | −0.489371 | ||||||||
\(130\) | −1.05688 | − | 0.964181i | −0.0926942 | − | 0.0845642i | ||||
\(131\) | −3.73904 | −0.326682 | −0.163341 | − | 0.986570i | \(-0.552227\pi\) | ||||
−0.163341 | + | 0.986570i | \(0.552227\pi\) | |||||||
\(132\) | − | 0.399656i | − | 0.0347856i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 11.4529 | 0.989379 | ||||||||
\(135\) | 4.57930 | − | 5.01955i | 0.394123 | − | 0.432014i | ||||
\(136\) | −14.7115 | −1.26150 | ||||||||
\(137\) | − | 2.36335i | − | 0.201914i | −0.994891 | − | 0.100957i | \(-0.967809\pi\) | ||
0.994891 | − | 0.100957i | \(-0.0321905\pi\) | |||||||
\(138\) | − | 2.08794i | − | 0.177737i | ||||||
\(139\) | −2.44279 | −0.207195 | −0.103597 | − | 0.994619i | \(-0.533035\pi\) | ||||
−0.103597 | + | 0.994619i | \(0.533035\pi\) | |||||||
\(140\) | −3.72897 | + | 4.08747i | −0.315156 | + | 0.345454i | ||||
\(141\) | −1.80703 | −0.152179 | ||||||||
\(142\) | − | 0.709852i | − | 0.0595695i | ||||||
\(143\) | − | 0.508722i | − | 0.0425415i | ||||||
\(144\) | −3.74694 | −0.312245 | ||||||||
\(145\) | −6.56665 | − | 5.99070i | −0.545330 | − | 0.497501i | ||||
\(146\) | 7.34588 | 0.607949 | ||||||||
\(147\) | 0.270726i | 0.0223291i | ||||||||
\(148\) | 3.91041i | 0.321433i | ||||||||
\(149\) | −14.2687 | −1.16894 | −0.584468 | − | 0.811417i | \(-0.698697\pi\) | ||||
−0.584468 | + | 0.811417i | \(0.698697\pi\) | |||||||
\(150\) | −0.254770 | − | 2.77154i | −0.0208019 | − | 0.226295i | ||||
\(151\) | −2.34319 | −0.190686 | −0.0953432 | − | 0.995444i | \(-0.530395\pi\) | ||||
−0.0953432 | + | 0.995444i | \(0.530395\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 13.1487i | − | 1.06301i | ||||||
\(154\) | 2.39043 | 0.192626 | ||||||||
\(155\) | 11.4425 | + | 10.4389i | 0.919081 | + | 0.838471i | ||||
\(156\) | −0.293122 | −0.0234686 | ||||||||
\(157\) | 16.1747i | 1.29088i | 0.763809 | + | 0.645442i | \(0.223327\pi\) | ||||
−0.763809 | + | 0.645442i | \(0.776673\pi\) | |||||||
\(158\) | − | 3.64451i | − | 0.289941i | ||||||
\(159\) | 7.26385 | 0.576061 | ||||||||
\(160\) | 6.98807 | − | 7.65990i | 0.552455 | − | 0.605568i | ||||
\(161\) | −10.2788 | −0.810083 | ||||||||
\(162\) | − | 6.84770i | − | 0.538006i | ||||||
\(163\) | − | 16.0258i | − | 1.25524i | −0.778521 | − | 0.627618i | \(-0.784030\pi\) | ||
0.778521 | − | 0.627618i | \(-0.215970\pi\) | |||||||
\(164\) | −4.80089 | −0.374886 | ||||||||
\(165\) | 0.667033 | − | 0.731162i | 0.0519285 | − | 0.0569209i | ||||
\(166\) | −5.21067 | −0.404426 | ||||||||
\(167\) | 7.57646i | 0.586284i | 0.956069 | + | 0.293142i | \(0.0947009\pi\) | ||||
−0.956069 | + | 0.293142i | \(0.905299\pi\) | |||||||
\(168\) | − | 4.42813i | − | 0.341638i | ||||||
\(169\) | 12.6269 | 0.971299 | ||||||||
\(170\) | −8.37155 | − | 7.63730i | −0.642069 | − | 0.585754i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 9.44344i | − | 0.720056i | ||||||
\(173\) | 8.86205i | 0.673769i | 0.941546 | + | 0.336885i | \(0.109373\pi\) | ||||
−0.941546 | + | 0.336885i | \(0.890627\pi\) | |||||||
\(174\) | 2.21275 | 0.167748 | ||||||||
\(175\) | −13.6441 | + | 1.25422i | −1.03140 | + | 0.0948099i | ||||
\(176\) | −1.14830 | −0.0865567 | ||||||||
\(177\) | − | 5.32370i | − | 0.400154i | ||||||
\(178\) | 6.16782i | 0.462297i | ||||||||
\(179\) | 5.46546 | 0.408508 | 0.204254 | − | 0.978918i | \(-0.434523\pi\) | ||||
0.204254 | + | 0.978918i | \(0.434523\pi\) | |||||||
\(180\) | 4.05351 | + | 3.69798i | 0.302130 | + | 0.275631i | ||||
\(181\) | −18.8164 | −1.39861 | −0.699306 | − | 0.714822i | \(-0.746508\pi\) | ||||
−0.699306 | + | 0.714822i | \(0.746508\pi\) | |||||||
\(182\) | − | 1.75323i | − | 0.129958i | ||||||
\(183\) | − | 4.82158i | − | 0.356422i | ||||||
\(184\) | 11.4049 | 0.840782 | ||||||||
\(185\) | −6.52654 | + | 7.15399i | −0.479840 | + | 0.525972i | ||||
\(186\) | −3.85575 | −0.282717 | ||||||||
\(187\) | − | 4.02960i | − | 0.294674i | ||||||
\(188\) | − | 3.07017i | − | 0.223915i | ||||||
\(189\) | 8.32680 | 0.605686 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.2606 | −1.24893 | −0.624465 | − | 0.781053i | \(-0.714683\pi\) | ||||
−0.624465 | + | 0.781053i | \(0.714683\pi\) | |||||||
\(192\) | 4.04667i | 0.292043i | ||||||||
\(193\) | − | 7.47422i | − | 0.538006i | −0.963139 | − | 0.269003i | \(-0.913306\pi\) | ||
0.963139 | − | 0.269003i | \(-0.0866942\pi\) | |||||||
\(194\) | −13.0284 | −0.935383 | ||||||||
\(195\) | −0.536260 | − | 0.489226i | −0.0384024 | − | 0.0350342i | ||||
\(196\) | −0.459968 | −0.0328549 | ||||||||
\(197\) | − | 12.2080i | − | 0.869784i | −0.900483 | − | 0.434892i | \(-0.856787\pi\) | ||
0.900483 | − | 0.434892i | \(-0.143213\pi\) | |||||||
\(198\) | − | 2.37056i | − | 0.168469i | ||||||
\(199\) | 7.75788 | 0.549942 | 0.274971 | − | 0.961453i | \(-0.411332\pi\) | ||||
0.274971 | + | 0.961453i | \(0.411332\pi\) | |||||||
\(200\) | 15.1389 | − | 1.39163i | 1.07049 | − | 0.0984029i | ||||
\(201\) | 5.81121 | 0.409891 | ||||||||
\(202\) | 18.5780i | 1.30715i | ||||||||
\(203\) | − | 10.8932i | − | 0.764556i | ||||||
\(204\) | −2.32183 | −0.162561 | ||||||||
\(205\) | −8.78311 | − | 8.01276i | −0.613439 | − | 0.559636i | ||||
\(206\) | 5.46586 | 0.380825 | ||||||||
\(207\) | 10.1934i | 0.708489i | ||||||||
\(208\) | 0.842208i | 0.0583966i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 2.29882 | − | 2.51983i | 0.158634 | − | 0.173885i | ||||
\(211\) | −10.0571 | −0.692359 | −0.346179 | − | 0.938168i | \(-0.612521\pi\) | ||||
−0.346179 | + | 0.938168i | \(0.612521\pi\) | |||||||
\(212\) | 12.3414i | 0.847612i | ||||||||
\(213\) | − | 0.360180i | − | 0.0246791i | ||||||
\(214\) | −15.9070 | −1.08738 | ||||||||
\(215\) | 15.7613 | − | 17.2766i | 1.07491 | − | 1.17825i | ||||
\(216\) | −9.23907 | −0.628639 | ||||||||
\(217\) | 18.9816i | 1.28856i | ||||||||
\(218\) | − | 4.10851i | − | 0.278264i | ||||||
\(219\) | 3.72731 | 0.251868 | ||||||||
\(220\) | 1.24226 | + | 1.13330i | 0.0837529 | + | 0.0764071i | ||||
\(221\) | −2.95545 | −0.198805 | ||||||||
\(222\) | − | 2.41067i | − | 0.161794i | ||||||
\(223\) | − | 28.3213i | − | 1.89654i | −0.317470 | − | 0.948268i | \(-0.602833\pi\) | ||
0.317470 | − | 0.948268i | \(-0.397167\pi\) | |||||||
\(224\) | 12.7068 | 0.849009 | ||||||||
\(225\) | 1.24379 | + | 13.5307i | 0.0829196 | + | 0.902049i | ||||
\(226\) | −4.16177 | −0.276837 | ||||||||
\(227\) | − | 15.8786i | − | 1.05390i | −0.849897 | − | 0.526949i | \(-0.823336\pi\) | ||
0.849897 | − | 0.526949i | \(-0.176664\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.3865 | −0.752438 | −0.376219 | − | 0.926531i | \(-0.622776\pi\) | ||||
−0.376219 | + | 0.926531i | \(0.622776\pi\) | |||||||
\(230\) | 6.48997 | + | 5.92075i | 0.427936 | + | 0.390403i | ||||
\(231\) | 1.21291 | 0.0798033 | ||||||||
\(232\) | 12.0867i | 0.793530i | ||||||||
\(233\) | − | 15.8642i | − | 1.03930i | −0.854379 | − | 0.519651i | \(-0.826062\pi\) | ||
0.854379 | − | 0.519651i | \(-0.173938\pi\) | |||||||
\(234\) | −1.73866 | −0.113660 | ||||||||
\(235\) | 5.12417 | − | 5.61680i | 0.334264 | − | 0.366400i | ||||
\(236\) | 9.04506 | 0.588783 | ||||||||
\(237\) | − | 1.84923i | − | 0.120120i | ||||||
\(238\) | − | 13.8873i | − | 0.900183i | ||||||
\(239\) | −20.8648 | −1.34963 | −0.674817 | − | 0.737985i | \(-0.735778\pi\) | ||||
−0.674817 | + | 0.737985i | \(0.735778\pi\) | |||||||
\(240\) | −1.10430 | + | 1.21047i | −0.0712822 | + | 0.0781352i | ||||
\(241\) | −28.4290 | −1.83127 | −0.915636 | − | 0.402008i | \(-0.868312\pi\) | ||||
−0.915636 | + | 0.402008i | \(0.868312\pi\) | |||||||
\(242\) | 10.7949i | 0.693925i | ||||||||
\(243\) | − | 12.5904i | − | 0.807673i | ||||||
\(244\) | 8.19195 | 0.524436 | ||||||||
\(245\) | −0.841501 | − | 0.767695i | −0.0537615 | − | 0.0490462i | ||||
\(246\) | 2.95963 | 0.188699 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | − | 21.0612i | − | 1.33739i | ||||||
\(249\) | −2.64390 | −0.167550 | ||||||||
\(250\) | 9.33726 | + | 7.06732i | 0.590540 | + | 0.446977i | ||||
\(251\) | 24.8136 | 1.56622 | 0.783109 | − | 0.621884i | \(-0.213632\pi\) | ||||
0.783109 | + | 0.621884i | \(0.213632\pi\) | |||||||
\(252\) | 6.72426i | 0.423588i | ||||||||
\(253\) | 3.12391i | 0.196399i | ||||||||
\(254\) | 9.62036 | 0.603635 | ||||||||
\(255\) | −4.24773 | − | 3.87517i | −0.266003 | − | 0.242673i | ||||
\(256\) | −16.5889 | −1.03681 | ||||||||
\(257\) | − | 5.44223i | − | 0.339477i | −0.985489 | − | 0.169739i | \(-0.945708\pi\) | ||
0.985489 | − | 0.169739i | \(-0.0542923\pi\) | |||||||
\(258\) | 5.82165i | 0.362440i | ||||||||
\(259\) | −11.8676 | −0.737415 | ||||||||
\(260\) | 0.831204 | − | 0.911115i | 0.0515491 | − | 0.0565050i | ||||
\(261\) | −10.8027 | −0.668671 | ||||||||
\(262\) | 3.91628i | 0.241949i | ||||||||
\(263\) | − | 19.5197i | − | 1.20363i | −0.798634 | − | 0.601817i | \(-0.794444\pi\) | ||
0.798634 | − | 0.601817i | \(-0.205556\pi\) | |||||||
\(264\) | −1.34579 | −0.0828276 | ||||||||
\(265\) | −20.5980 | + | 22.5783i | −1.26533 | + | 1.38697i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.12956i | 0.191526i | ||||||||
\(268\) | 9.87334i | 0.603110i | ||||||||
\(269\) | 18.5848 | 1.13314 | 0.566568 | − | 0.824015i | \(-0.308271\pi\) | ||||
0.566568 | + | 0.824015i | \(0.308271\pi\) | |||||||
\(270\) | −5.25749 | − | 4.79637i | −0.319961 | − | 0.291898i | ||||
\(271\) | 1.89214 | 0.114939 | 0.0574696 | − | 0.998347i | \(-0.481697\pi\) | ||||
0.0574696 | + | 0.998347i | \(0.481697\pi\) | |||||||
\(272\) | 6.67115i | 0.404498i | ||||||||
\(273\) | − | 0.889588i | − | 0.0538403i | ||||||
\(274\) | −2.47538 | −0.149543 | ||||||||
\(275\) | 0.381179 | + | 4.14669i | 0.0229860 | + | 0.250055i | ||||
\(276\) | 1.79998 | 0.108346 | ||||||||
\(277\) | 6.77887i | 0.407303i | 0.979043 | + | 0.203652i | \(0.0652810\pi\) | ||||
−0.979043 | + | 0.203652i | \(0.934719\pi\) | |||||||
\(278\) | 2.55859i | 0.153454i | ||||||||
\(279\) | 18.8239 | 1.12696 | ||||||||
\(280\) | 13.7640 | + | 12.5568i | 0.822557 | + | 0.750413i | ||||
\(281\) | 12.2861 | 0.732927 | 0.366464 | − | 0.930432i | \(-0.380568\pi\) | ||||
0.366464 | + | 0.930432i | \(0.380568\pi\) | |||||||
\(282\) | 1.89268i | 0.112708i | ||||||||
\(283\) | 25.6667i | 1.52572i | 0.646561 | + | 0.762862i | \(0.276207\pi\) | ||||
−0.646561 | + | 0.762862i | \(0.723793\pi\) | |||||||
\(284\) | 0.611952 | 0.0363126 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.532837 | −0.0315073 | ||||||||
\(287\) | − | 14.5701i | − | 0.860044i | ||||||
\(288\) | − | 12.6012i | − | 0.742534i | ||||||
\(289\) | −6.41023 | −0.377072 | ||||||||
\(290\) | −6.27468 | + | 6.87792i | −0.368462 | + | 0.403885i | ||||
\(291\) | −6.61061 | −0.387521 | ||||||||
\(292\) | 6.33276i | 0.370597i | ||||||||
\(293\) | 28.1121i | 1.64232i | 0.570695 | + | 0.821162i | \(0.306674\pi\) | ||||
−0.570695 | + | 0.821162i | \(0.693326\pi\) | |||||||
\(294\) | 0.283559 | 0.0165375 | ||||||||
\(295\) | 16.5477 | + | 15.0964i | 0.963446 | + | 0.878944i | ||||
\(296\) | 13.1678 | 0.765361 | ||||||||
\(297\) | − | 2.53067i | − | 0.146844i | ||||||
\(298\) | 14.9451i | 0.865744i | ||||||||
\(299\) | 2.29119 | 0.132503 | ||||||||
\(300\) | 2.38930 | − | 0.219633i | 0.137946 | − | 0.0126805i | ||||
\(301\) | 28.6596 | 1.65191 | ||||||||
\(302\) | 2.45427i | 0.141227i | ||||||||
\(303\) | 9.42651i | 0.541539i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.9870 | + | 13.6725i | 0.858152 | + | 0.782886i | ||||
\(306\) | −13.7719 | −0.787290 | ||||||||
\(307\) | − | 2.57676i | − | 0.147064i | −0.997293 | − | 0.0735319i | \(-0.976573\pi\) | ||
0.997293 | − | 0.0735319i | \(-0.0234271\pi\) | |||||||
\(308\) | 2.06075i | 0.117422i | ||||||||
\(309\) | 2.77338 | 0.157772 | ||||||||
\(310\) | 10.9337 | − | 11.9849i | 0.620993 | − | 0.680695i | ||||
\(311\) | 14.6367 | 0.829974 | 0.414987 | − | 0.909827i | \(-0.363786\pi\) | ||||
0.414987 | + | 0.909827i | \(0.363786\pi\) | |||||||
\(312\) | 0.987050i | 0.0558807i | ||||||||
\(313\) | 1.49408i | 0.0844507i | 0.999108 | + | 0.0422253i | \(0.0134447\pi\) | ||||
−0.999108 | + | 0.0422253i | \(0.986555\pi\) | |||||||
\(314\) | 16.9415 | 0.956062 | ||||||||
\(315\) | −11.2229 | + | 12.3019i | −0.632339 | + | 0.693132i | ||||
\(316\) | 3.14187 | 0.176744 | ||||||||
\(317\) | 5.64234i | 0.316905i | 0.987367 | + | 0.158453i | \(0.0506505\pi\) | ||||
−0.987367 | + | 0.158453i | \(0.949349\pi\) | |||||||
\(318\) | − | 7.60818i | − | 0.426646i | ||||||
\(319\) | −3.31065 | −0.185361 | ||||||||
\(320\) | −12.5783 | − | 11.4751i | −0.703148 | − | 0.641477i | ||||
\(321\) | −8.07124 | −0.450493 | ||||||||
\(322\) | 10.7660i | 0.599968i | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 5.90329 | 0.327960 | ||||||||
\(325\) | 3.04133 | − | 0.279570i | 0.168703 | − | 0.0155078i | ||||
\(326\) | −16.7854 | −0.929660 | ||||||||
\(327\) | − | 2.08466i | − | 0.115282i | ||||||
\(328\) | 16.1663i | 0.892637i | ||||||||
\(329\) | 9.31757 | 0.513694 | ||||||||
\(330\) | −0.765821 | − | 0.698653i | −0.0421570 | − | 0.0384596i | ||||
\(331\) | −31.8920 | −1.75294 | −0.876472 | − | 0.481452i | \(-0.840110\pi\) | ||||
−0.876472 | + | 0.481452i | \(0.840110\pi\) | |||||||
\(332\) | − | 4.49203i | − | 0.246532i | ||||||
\(333\) | 11.7690i | 0.644935i | ||||||||
\(334\) | 7.93561 | 0.434217 | ||||||||
\(335\) | −16.4788 | + | 18.0630i | −0.900331 | + | 0.986889i | ||||
\(336\) | −2.00801 | −0.109546 | ||||||||
\(337\) | 15.3378i | 0.835504i | 0.908561 | + | 0.417752i | \(0.137182\pi\) | ||||
−0.908561 | + | 0.417752i | \(0.862818\pi\) | |||||||
\(338\) | − | 13.2254i | − | 0.719369i | ||||||
\(339\) | −2.11169 | −0.114691 | ||||||||
\(340\) | 6.58399 | − | 7.21697i | 0.357067 | − | 0.391395i | ||||
\(341\) | 5.76886 | 0.312401 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.7864i | 0.960373i | ||||||||
\(344\) | −31.7995 | −1.71452 | ||||||||
\(345\) | 3.29302 | + | 3.00419i | 0.177290 | + | 0.161740i | ||||
\(346\) | 9.28214 | 0.499011 | ||||||||
\(347\) | 0.0826977i | 0.00443945i | 0.999998 | + | 0.00221972i | \(0.000706560\pi\) | ||||
−0.999998 | + | 0.00221972i | \(0.999293\pi\) | |||||||
\(348\) | 1.90758i | 0.102257i | ||||||||
\(349\) | 4.64333 | 0.248552 | 0.124276 | − | 0.992248i | \(-0.460339\pi\) | ||||
0.124276 | + | 0.992248i | \(0.460339\pi\) | |||||||
\(350\) | 1.31367 | + | 14.2909i | 0.0702186 | + | 0.763880i | ||||
\(351\) | −1.85608 | −0.0990702 | ||||||||
\(352\) | − | 3.86183i | − | 0.205836i | ||||||
\(353\) | 3.99402i | 0.212580i | 0.994335 | + | 0.106290i | \(0.0338972\pi\) | ||||
−0.994335 | + | 0.106290i | \(0.966103\pi\) | |||||||
\(354\) | −5.57606 | −0.296364 | ||||||||
\(355\) | 1.11955 | + | 1.02136i | 0.0594196 | + | 0.0542080i | ||||
\(356\) | −5.31717 | −0.281809 | ||||||||
\(357\) | − | 7.04645i | − | 0.372938i | ||||||
\(358\) | − | 5.72454i | − | 0.302551i | ||||||
\(359\) | −30.2198 | −1.59494 | −0.797471 | − | 0.603358i | \(-0.793829\pi\) | ||||
−0.797471 | + | 0.603358i | \(0.793829\pi\) | |||||||
\(360\) | 12.4525 | − | 13.6496i | 0.656302 | − | 0.719399i | ||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 19.7084i | 1.03585i | ||||||||
\(363\) | 5.47736i | 0.287487i | ||||||||
\(364\) | 1.51143 | 0.0792202 | ||||||||
\(365\) | −10.5695 | + | 11.5856i | −0.553232 | + | 0.606420i | ||||
\(366\) | −5.05014 | −0.263975 | ||||||||
\(367\) | − | 18.1399i | − | 0.946896i | −0.880822 | − | 0.473448i | \(-0.843009\pi\) | ||
0.880822 | − | 0.473448i | \(-0.156991\pi\) | |||||||
\(368\) | − | 5.17175i | − | 0.269596i | ||||||
\(369\) | −14.4490 | −0.752185 | ||||||||
\(370\) | 7.49311 | + | 6.83591i | 0.389548 | + | 0.355382i | ||||
\(371\) | −37.4546 | −1.94455 | ||||||||
\(372\) | − | 3.32398i | − | 0.172340i | ||||||
\(373\) | 25.2151i | 1.30559i | 0.757536 | + | 0.652794i | \(0.226403\pi\) | ||||
−0.757536 | + | 0.652794i | \(0.773597\pi\) | |||||||
\(374\) | −4.22061 | −0.218243 | ||||||||
\(375\) | 4.73774 | + | 3.58597i | 0.244656 | + | 0.185179i | ||||
\(376\) | −10.3384 | −0.533161 | ||||||||
\(377\) | 2.42815i | 0.125056i | ||||||||
\(378\) | − | 8.72152i | − | 0.448586i | ||||||
\(379\) | −27.5634 | −1.41584 | −0.707918 | − | 0.706294i | \(-0.750366\pi\) | ||||
−0.707918 | + | 0.706294i | \(0.750366\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.88138 | 0.250081 | ||||||||
\(382\) | 18.0788i | 0.924990i | ||||||||
\(383\) | − | 18.3237i | − | 0.936296i | −0.883650 | − | 0.468148i | \(-0.844921\pi\) | ||
0.883650 | − | 0.468148i | \(-0.155079\pi\) | |||||||
\(384\) | −0.690166 | −0.0352199 | ||||||||
\(385\) | −3.43942 | + | 3.77009i | −0.175289 | + | 0.192141i | ||||
\(386\) | −7.82852 | −0.398461 | ||||||||
\(387\) | − | 28.4215i | − | 1.44474i | ||||||
\(388\) | − | 11.2315i | − | 0.570195i | ||||||
\(389\) | 7.18503 | 0.364296 | 0.182148 | − | 0.983271i | \(-0.441695\pi\) | ||||
0.182148 | + | 0.983271i | \(0.441695\pi\) | |||||||
\(390\) | −0.512417 | + | 0.561680i | −0.0259472 | + | 0.0284418i | ||||
\(391\) | 18.1486 | 0.917813 | ||||||||
\(392\) | 1.54888i | 0.0782303i | ||||||||
\(393\) | 1.98713i | 0.100237i | ||||||||
\(394\) | −12.7867 | −0.644184 | ||||||||
\(395\) | 5.74797 | + | 5.24383i | 0.289212 | + | 0.263846i | ||||
\(396\) | 2.04362 | 0.102696 | ||||||||
\(397\) | 11.7242i | 0.588423i | 0.955740 | + | 0.294211i | \(0.0950570\pi\) | ||||
−0.955740 | + | 0.294211i | \(0.904943\pi\) | |||||||
\(398\) | − | 8.12562i | − | 0.407301i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.631056 | − | 6.86500i | −0.0315528 | − | 0.343250i | ||||
\(401\) | −39.2123 | −1.95817 | −0.979085 | − | 0.203451i | \(-0.934784\pi\) | ||||
−0.979085 | + | 0.203451i | \(0.934784\pi\) | |||||||
\(402\) | − | 6.08667i | − | 0.303576i | ||||||
\(403\) | − | 4.23108i | − | 0.210765i | ||||||
\(404\) | −16.0158 | −0.796816 | ||||||||
\(405\) | 10.7999 | + | 9.85268i | 0.536652 | + | 0.489584i | ||||
\(406\) | −11.4096 | −0.566249 | ||||||||
\(407\) | 3.60677i | 0.178781i | ||||||||
\(408\) | 7.81845i | 0.387071i | ||||||||
\(409\) | 8.87630 | 0.438905 | 0.219452 | − | 0.975623i | \(-0.429573\pi\) | ||||
0.219452 | + | 0.975623i | \(0.429573\pi\) | |||||||
\(410\) | −8.39259 | + | 9.19945i | −0.414481 | + | 0.454329i | ||||
\(411\) | −1.25601 | −0.0619543 | ||||||||
\(412\) | 4.71203i | 0.232145i | ||||||||
\(413\) | 27.4506i | 1.35076i | ||||||||
\(414\) | 10.6766 | 0.524725 | ||||||||
\(415\) | 7.49727 | − | 8.21806i | 0.368027 | − | 0.403409i | ||||
\(416\) | −2.83240 | −0.138870 | ||||||||
\(417\) | 1.29823i | 0.0635745i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.80196 | 0.381151 | 0.190575 | − | 0.981673i | \(-0.438965\pi\) | ||||
0.190575 | + | 0.981673i | \(0.438965\pi\) | |||||||
\(420\) | 2.17230 | + | 1.98177i | 0.105997 | + | 0.0967006i | ||||
\(421\) | −34.5570 | −1.68421 | −0.842104 | − | 0.539316i | \(-0.818683\pi\) | ||||
−0.842104 | + | 0.539316i | \(0.818683\pi\) | |||||||
\(422\) | 10.5338i | 0.512779i | ||||||||
\(423\) | − | 9.24014i | − | 0.449271i | ||||||
\(424\) | 41.5580 | 2.01824 | ||||||||
\(425\) | 24.0905 | − | 2.21448i | 1.16856 | − | 0.107418i | ||||
\(426\) | −0.377253 | −0.0182780 | ||||||||
\(427\) | 24.8615i | 1.20313i | ||||||||
\(428\) | − | 13.7132i | − | 0.662851i | ||||||
\(429\) | −0.270362 | −0.0130532 | ||||||||
\(430\) | −18.0955 | − | 16.5084i | −0.872643 | − | 0.796105i | ||||
\(431\) | −2.83951 | −0.136775 | −0.0683873 | − | 0.997659i | \(-0.521785\pi\) | ||||
−0.0683873 | + | 0.997659i | \(0.521785\pi\) | |||||||
\(432\) | 4.18961i | 0.201573i | ||||||||
\(433\) | 21.8527i | 1.05018i | 0.851048 | + | 0.525088i | \(0.175967\pi\) | ||||
−0.851048 | + | 0.525088i | \(0.824033\pi\) | |||||||
\(434\) | 19.8814 | 0.954338 | ||||||||
\(435\) | −3.18378 | + | 3.48986i | −0.152650 | + | 0.167326i | ||||
\(436\) | 3.54188 | 0.169625 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | − | 3.90399i | − | 0.186540i | ||||||
\(439\) | 32.5760 | 1.55477 | 0.777383 | − | 0.629027i | \(-0.216547\pi\) | ||||
0.777383 | + | 0.629027i | \(0.216547\pi\) | |||||||
\(440\) | 3.81624 | − | 4.18313i | 0.181932 | − | 0.199423i | ||||
\(441\) | −1.38434 | −0.0659212 | ||||||||
\(442\) | 3.09555i | 0.147240i | ||||||||
\(443\) | 7.76173i | 0.368771i | 0.982854 | + | 0.184385i | \(0.0590295\pi\) | ||||
−0.982854 | + | 0.184385i | \(0.940971\pi\) | |||||||
\(444\) | 2.07820 | 0.0986269 | ||||||||
\(445\) | −9.72763 | − | 8.87444i | −0.461134 | − | 0.420689i | ||||
\(446\) | −29.6638 | −1.40462 | ||||||||
\(447\) | 7.58313i | 0.358670i | ||||||||
\(448\) | − | 20.8658i | − | 0.985817i | ||||||
\(449\) | 22.9821 | 1.08459 | 0.542296 | − | 0.840187i | \(-0.317555\pi\) | ||||
0.542296 | + | 0.840187i | \(0.317555\pi\) | |||||||
\(450\) | 14.1721 | − | 1.30275i | 0.668081 | − | 0.0614124i | ||||
\(451\) | −4.42811 | −0.208511 | ||||||||
\(452\) | − | 3.58779i | − | 0.168756i | ||||||
\(453\) | 1.24530i | 0.0585092i | ||||||||
\(454\) | −16.6312 | −0.780543 | ||||||||
\(455\) | 2.76512 | + | 2.52260i | 0.129631 | + | 0.118261i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 3.38866i | − | 0.158515i | −0.996854 | − | 0.0792573i | \(-0.974745\pi\) | ||
0.996854 | − | 0.0792573i | \(-0.0252549\pi\) | |||||||
\(458\) | 11.9262i | 0.557275i | ||||||||
\(459\) | −14.7021 | −0.686234 | ||||||||
\(460\) | −5.10418 | + | 5.59489i | −0.237983 | + | 0.260863i | ||||
\(461\) | −10.8529 | −0.505471 | −0.252735 | − | 0.967535i | \(-0.581330\pi\) | ||||
−0.252735 | + | 0.967535i | \(0.581330\pi\) | |||||||
\(462\) | − | 1.27040i | − | 0.0591044i | ||||||
\(463\) | 7.31171i | 0.339804i | 0.985461 | + | 0.169902i | \(0.0543451\pi\) | ||||
−0.985461 | + | 0.169902i | \(0.945655\pi\) | |||||||
\(464\) | 5.48090 | 0.254445 | ||||||||
\(465\) | 5.54777 | − | 6.08114i | 0.257272 | − | 0.282006i | ||||
\(466\) | −16.6163 | −0.769733 | ||||||||
\(467\) | 10.8418i | 0.501699i | 0.968026 | + | 0.250850i | \(0.0807100\pi\) | ||||
−0.968026 | + | 0.250850i | \(0.919290\pi\) | |||||||
\(468\) | − | 1.49887i | − | 0.0692851i | ||||||
\(469\) | −29.9643 | −1.38362 | ||||||||
\(470\) | −5.88305 | − | 5.36706i | −0.271365 | − | 0.247564i | ||||
\(471\) | 8.59612 | 0.396088 | ||||||||
\(472\) | − | 30.4580i | − | 1.40194i | ||||||
\(473\) | − | 8.71018i | − | 0.400494i | ||||||
\(474\) | −1.93688 | −0.0889640 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 11.9720 | 0.548738 | ||||||||
\(477\) | 37.1433i | 1.70068i | ||||||||
\(478\) | 21.8539i | 0.999574i | ||||||||
\(479\) | −3.44738 | −0.157515 | −0.0787574 | − | 0.996894i | \(-0.525095\pi\) | ||||
−0.0787574 | + | 0.996894i | \(0.525095\pi\) | |||||||
\(480\) | −4.07088 | − | 3.71383i | −0.185809 | − | 0.169512i | ||||
\(481\) | 2.64533 | 0.120617 | ||||||||
\(482\) | 29.7766i | 1.35629i | ||||||||
\(483\) | 5.46270i | 0.248561i | ||||||||
\(484\) | −9.30613 | −0.423006 | ||||||||
\(485\) | 18.7456 | − | 20.5478i | 0.851195 | − | 0.933029i | ||||
\(486\) | −13.1872 | −0.598183 | ||||||||
\(487\) | 26.9972i | 1.22336i | 0.791106 | + | 0.611680i | \(0.209506\pi\) | ||||
−0.791106 | + | 0.611680i | \(0.790494\pi\) | |||||||
\(488\) | − | 27.5853i | − | 1.24873i | ||||||
\(489\) | −8.51695 | −0.385150 | ||||||||
\(490\) | −0.804086 | + | 0.881390i | −0.0363249 | + | 0.0398172i | ||||
\(491\) | 0.243979 | 0.0110106 | 0.00550530 | − | 0.999985i | \(-0.498248\pi\) | ||||
0.00550530 | + | 0.999985i | \(0.498248\pi\) | |||||||
\(492\) | 2.55145i | 0.115028i | ||||||||
\(493\) | 19.2334i | 0.866231i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.73876 | + | 3.41084i | 0.168045 | + | 0.153306i | ||||
\(496\) | −9.55055 | −0.428832 | ||||||||
\(497\) | 1.85719i | 0.0833065i | ||||||||
\(498\) | 2.76923i | 0.124092i | ||||||||
\(499\) | 3.24868 | 0.145431 | 0.0727155 | − | 0.997353i | \(-0.476833\pi\) | ||||
0.0727155 | + | 0.997353i | \(0.476833\pi\) | |||||||
\(500\) | −6.09262 | + | 8.04949i | −0.272470 | + | 0.359984i | ||||
\(501\) | 4.02653 | 0.179892 | ||||||||
\(502\) | − | 25.9898i | − | 1.15998i | ||||||
\(503\) | 7.12545i | 0.317708i | 0.987302 | + | 0.158854i | \(0.0507799\pi\) | ||||
−0.987302 | + | 0.158854i | \(0.949220\pi\) | |||||||
\(504\) | 22.6430 | 1.00860 | ||||||||
\(505\) | −29.3005 | − | 26.7306i | −1.30386 | − | 1.18950i | ||||
\(506\) | 3.27199 | 0.145458 | ||||||||
\(507\) | − | 6.71060i | − | 0.298028i | ||||||
\(508\) | 8.29355i | 0.367967i | ||||||||
\(509\) | 1.73022 | 0.0766907 | 0.0383453 | − | 0.999265i | \(-0.487791\pi\) | ||||
0.0383453 | + | 0.999265i | \(0.487791\pi\) | |||||||
\(510\) | −4.05887 | + | 4.44909i | −0.179730 | + | 0.197009i | ||||
\(511\) | −19.2191 | −0.850203 | ||||||||
\(512\) | 14.7780i | 0.653100i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.70021 | −0.251426 | ||||||||
\(515\) | −7.86445 | + | 8.62054i | −0.346549 | + | 0.379866i | ||||
\(516\) | −5.01875 | −0.220938 | ||||||||
\(517\) | − | 2.83178i | − | 0.124541i | ||||||
\(518\) | 12.4301i | 0.546149i | ||||||||
\(519\) | 4.70977 | 0.206736 | ||||||||
\(520\) | −3.06806 | − | 2.79897i | −0.134543 | − | 0.122743i | ||||
\(521\) | −12.8033 | −0.560922 | −0.280461 | − | 0.959865i | \(-0.590487\pi\) | ||||
−0.280461 | + | 0.959865i | \(0.590487\pi\) | |||||||
\(522\) | 11.3148i | 0.495235i | ||||||||
\(523\) | − | 8.71641i | − | 0.381142i | −0.981673 | − | 0.190571i | \(-0.938966\pi\) | ||
0.981673 | − | 0.190571i | \(-0.0610340\pi\) | |||||||
\(524\) | −3.37616 | −0.147488 | ||||||||
\(525\) | 0.666558 | + | 7.25121i | 0.0290910 | + | 0.316469i | ||||
\(526\) | −20.4449 | −0.891441 | ||||||||
\(527\) | − | 33.5145i | − | 1.45992i | ||||||
\(528\) | 0.610270i | 0.0265586i | ||||||||
\(529\) | 8.93048 | 0.388282 | ||||||||
\(530\) | 23.6486 | + | 21.5744i | 1.02723 | + | 0.937133i | ||||
\(531\) | 27.2225 | 1.18136 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.24773i | 0.140675i | ||||||||
\(534\) | 3.27790 | 0.141849 | ||||||||
\(535\) | 22.8875 | − | 25.0879i | 0.989514 | − | 1.08465i | ||||
\(536\) | 33.2471 | 1.43606 | ||||||||
\(537\) | − | 2.90463i | − | 0.125344i | ||||||
\(538\) | − | 19.4658i | − | 0.839230i | ||||||
\(539\) | −0.424253 | −0.0182739 | ||||||||
\(540\) | 4.13487 | − | 4.53239i | 0.177936 | − | 0.195043i | ||||
\(541\) | 11.0154 | 0.473588 | 0.236794 | − | 0.971560i | \(-0.423903\pi\) | ||||
0.236794 | + | 0.971560i | \(0.423903\pi\) | |||||||
\(542\) | − | 1.98183i | − | 0.0851268i | ||||||
\(543\) | 10.0000i | 0.429143i | ||||||||
\(544\) | −22.4355 | −0.961916 | ||||||||
\(545\) | 6.47978 | + | 5.91146i | 0.277563 | + | 0.253219i | ||||
\(546\) | −0.931757 | −0.0398755 | ||||||||
\(547\) | − | 18.3959i | − | 0.786551i | −0.919421 | − | 0.393275i | \(-0.871342\pi\) | ||
0.919421 | − | 0.393275i | \(-0.128658\pi\) | |||||||
\(548\) | − | 2.13398i | − | 0.0911591i | ||||||
\(549\) | 24.6549 | 1.05225 | ||||||||
\(550\) | 4.34326 | − | 0.399248i | 0.185197 | − | 0.0170240i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | − | 6.06118i | − | 0.257981i | ||||||
\(553\) | 9.53516i | 0.405476i | ||||||||
\(554\) | 7.10021 | 0.301659 | ||||||||
\(555\) | 3.80201 | + | 3.46855i | 0.161386 | + | 0.147232i | ||||
\(556\) | −2.20571 | −0.0935431 | ||||||||
\(557\) | − | 0.202098i | − | 0.00856316i | −0.999991 | − | 0.00428158i | \(-0.998637\pi\) | ||
0.999991 | − | 0.00428158i | \(-0.00136287\pi\) | |||||||
\(558\) | − | 19.7162i | − | 0.834653i | ||||||
\(559\) | −6.38835 | −0.270199 | ||||||||
\(560\) | 5.69409 | − | 6.24152i | 0.240619 | − | 0.263752i | ||||
\(561\) | −2.14154 | −0.0904161 | ||||||||
\(562\) | − | 12.8685i | − | 0.542824i | ||||||
\(563\) | 6.76375i | 0.285058i | 0.989791 | + | 0.142529i | \(0.0455234\pi\) | ||||
−0.989791 | + | 0.142529i | \(0.954477\pi\) | |||||||
\(564\) | −1.63165 | −0.0687049 | ||||||||
\(565\) | 5.98809 | − | 6.56378i | 0.251921 | − | 0.276140i | ||||
\(566\) | 26.8833 | 1.12999 | ||||||||
\(567\) | 17.9157i | 0.752389i | ||||||||
\(568\) | − | 2.06066i | − | 0.0864636i | ||||||
\(569\) | 7.15701 | 0.300038 | 0.150019 | − | 0.988683i | \(-0.452067\pi\) | ||||
0.150019 | + | 0.988683i | \(0.452067\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.3153 | −0.766471 | −0.383236 | − | 0.923651i | \(-0.625190\pi\) | ||||
−0.383236 | + | 0.923651i | \(0.625190\pi\) | |||||||
\(572\) | − | 0.459349i | − | 0.0192064i | ||||||
\(573\) | 9.17318i | 0.383215i | ||||||||
\(574\) | −15.2607 | −0.636971 | ||||||||
\(575\) | −18.6759 | + | 1.71676i | −0.778841 | + | 0.0715938i | ||||
\(576\) | −20.6924 | −0.862184 | ||||||||
\(577\) | 21.5794i | 0.898364i | 0.893440 | + | 0.449182i | \(0.148284\pi\) | ||||
−0.893440 | + | 0.449182i | \(0.851716\pi\) | |||||||
\(578\) | 6.71409i | 0.279269i | ||||||||
\(579\) | −3.97220 | −0.165079 | ||||||||
\(580\) | −5.92934 | − | 5.40929i | −0.246202 | − | 0.224609i | ||||
\(581\) | 13.6327 | 0.565581 | ||||||||
\(582\) | 6.92397i | 0.287008i | ||||||||
\(583\) | 11.3831i | 0.471441i | ||||||||
\(584\) | 21.3247 | 0.882423 | ||||||||
\(585\) | 2.50163 | − | 2.74214i | 0.103430 | − | 0.113373i | ||||
\(586\) | 29.4446 | 1.21635 | ||||||||
\(587\) | − | 28.9431i | − | 1.19461i | −0.802014 | − | 0.597305i | \(-0.796238\pi\) | ||
0.802014 | − | 0.597305i | \(-0.203762\pi\) | |||||||
\(588\) | 0.244452i | 0.0100810i | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 15.8120 | − | 17.3321i | 0.650969 | − | 0.713553i | ||||
\(591\) | −6.48798 | −0.266880 | ||||||||
\(592\) | − | 5.97114i | − | 0.245412i | ||||||
\(593\) | 17.8231i | 0.731907i | 0.930633 | + | 0.365954i | \(0.119257\pi\) | ||||
−0.930633 | + | 0.365954i | \(0.880743\pi\) | |||||||
\(594\) | −2.65063 | −0.108756 | ||||||||
\(595\) | 21.9026 | + | 19.9815i | 0.897918 | + | 0.819164i | ||||
\(596\) | −12.8839 | −0.527744 | ||||||||
\(597\) | − | 4.12295i | − | 0.168741i | ||||||
\(598\) | − | 2.39980i | − | 0.0981350i | ||||||
\(599\) | −8.55080 | −0.349376 | −0.174688 | − | 0.984624i | \(-0.555892\pi\) | ||||
−0.174688 | + | 0.984624i | \(0.555892\pi\) | |||||||
\(600\) | −0.739584 | − | 8.04564i | −0.0301934 | − | 0.328462i | ||||
\(601\) | 4.19029 | 0.170925 | 0.0854627 | − | 0.996341i | \(-0.472763\pi\) | ||||
0.0854627 | + | 0.996341i | \(0.472763\pi\) | |||||||
\(602\) | − | 30.0182i | − | 1.22345i | ||||||
\(603\) | 29.7153i | 1.21010i | ||||||||
\(604\) | −2.11578 | −0.0860899 | ||||||||
\(605\) | −17.0253 | − | 15.5321i | −0.692178 | − | 0.631469i | ||||
\(606\) | 9.87335 | 0.401077 | ||||||||
\(607\) | 7.59458i | 0.308254i | 0.988051 | + | 0.154127i | \(0.0492566\pi\) | ||||
−0.988051 | + | 0.154127i | \(0.950743\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.78925 | −0.234592 | ||||||||
\(610\) | 14.3206 | − | 15.6974i | 0.579825 | − | 0.635569i | ||||
\(611\) | −2.07693 | −0.0840234 | ||||||||
\(612\) | − | 11.8726i | − | 0.479920i | ||||||
\(613\) | 17.9449i | 0.724788i | 0.932025 | + | 0.362394i | \(0.118041\pi\) | ||||
−0.932025 | + | 0.362394i | \(0.881959\pi\) | |||||||
\(614\) | −2.69891 | −0.108919 | ||||||||
\(615\) | −4.25841 | + | 4.66781i | −0.171716 | + | 0.188224i | ||||
\(616\) | 6.93929 | 0.279592 | ||||||||
\(617\) | − | 40.5840i | − | 1.63385i | −0.576745 | − | 0.816924i | \(-0.695677\pi\) | ||
0.576745 | − | 0.816924i | \(-0.304323\pi\) | |||||||
\(618\) | − | 2.90485i | − | 0.116850i | ||||||
\(619\) | 25.5608 | 1.02738 | 0.513688 | − | 0.857977i | \(-0.328279\pi\) | ||||
0.513688 | + | 0.857977i | \(0.328279\pi\) | |||||||
\(620\) | 10.3320 | + | 9.42576i | 0.414941 | + | 0.378548i | ||||
\(621\) | 11.3976 | 0.457372 | ||||||||
\(622\) | − | 15.3306i | − | 0.614700i | ||||||
\(623\) | − | 16.1369i | − | 0.646512i | ||||||
\(624\) | 0.447594 | 0.0179181 | ||||||||
\(625\) | −24.5810 | + | 4.55767i | −0.983242 | + | 0.182307i | ||||
\(626\) | 1.56491 | 0.0625463 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.6049i | 0.582801i | ||||||||
\(629\) | 20.9538 | 0.835481 | ||||||||
\(630\) | 12.8850 | + | 11.7549i | 0.513351 | + | 0.468326i | ||||
\(631\) | 4.63486 | 0.184511 | 0.0922555 | − | 0.995735i | \(-0.470592\pi\) | ||||
0.0922555 | + | 0.995735i | \(0.470592\pi\) | |||||||
\(632\) | − | 10.5798i | − | 0.420842i | ||||||
\(633\) | 5.34487i | 0.212440i | ||||||||
\(634\) | 5.90980 | 0.234708 | ||||||||
\(635\) | −13.8421 | + | 15.1728i | −0.549306 | + | 0.602116i | ||||
\(636\) | 6.55888 | 0.260077 | ||||||||
\(637\) | 0.311162i | 0.0123287i | ||||||||
\(638\) | 3.46758i | 0.137283i | ||||||||
\(639\) | 1.84176 | 0.0728589 | ||||||||
\(640\) | 1.95710 | − | 2.14525i | 0.0773610 | − | 0.0847985i | ||||
\(641\) | −23.2079 | −0.916658 | −0.458329 | − | 0.888783i | \(-0.651552\pi\) | ||||
−0.458329 | + | 0.888783i | \(0.651552\pi\) | |||||||
\(642\) | 8.45384i | 0.333646i | ||||||||
\(643\) | 15.2454i | 0.601219i | 0.953747 | + | 0.300610i | \(0.0971902\pi\) | ||||
−0.953747 | + | 0.300610i | \(0.902810\pi\) | |||||||
\(644\) | −9.28122 | −0.365731 | ||||||||
\(645\) | −9.18168 | − | 8.37638i | −0.361528 | − | 0.329819i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 17.6749i | − | 0.694872i | −0.937704 | − | 0.347436i | \(-0.887052\pi\) | ||
0.937704 | − | 0.347436i | \(-0.112948\pi\) | |||||||
\(648\) | − | 19.8785i | − | 0.780902i | ||||||
\(649\) | 8.34273 | 0.327481 | ||||||||
\(650\) | −0.292823 | − | 3.18550i | −0.0114855 | − | 0.124946i | ||||
\(651\) | 10.0878 | 0.395374 | ||||||||
\(652\) | − | 14.4704i | − | 0.566706i | ||||||
\(653\) | − | 6.86456i | − | 0.268631i | −0.990939 | − | 0.134315i | \(-0.957116\pi\) | ||
0.990939 | − | 0.134315i | \(-0.0428835\pi\) | |||||||
\(654\) | −2.18348 | −0.0853809 | ||||||||
\(655\) | −6.17661 | − | 5.63487i | −0.241340 | − | 0.220173i | ||||
\(656\) | 7.33089 | 0.286223 | ||||||||
\(657\) | 19.0594i | 0.743578i | ||||||||
\(658\) | − | 9.75924i | − | 0.380455i | ||||||
\(659\) | 27.3966 | 1.06722 | 0.533611 | − | 0.845730i | \(-0.320835\pi\) | ||||
0.533611 | + | 0.845730i | \(0.320835\pi\) | |||||||
\(660\) | 0.602296 | − | 0.660201i | 0.0234444 | − | 0.0256983i | ||||
\(661\) | −28.5502 | −1.11048 | −0.555238 | − | 0.831692i | \(-0.687373\pi\) | ||||
−0.555238 | + | 0.831692i | \(0.687373\pi\) | |||||||
\(662\) | 33.4038i | 1.29828i | ||||||||
\(663\) | 1.57068i | 0.0610003i | ||||||||
\(664\) | −15.1263 | −0.587014 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 12.3268 | 0.477655 | ||||||||
\(667\) | − | 14.9106i | − | 0.577339i | ||||||
\(668\) | 6.84115i | 0.264692i | ||||||||
\(669\) | −15.0515 | −0.581923 | ||||||||
\(670\) | 18.9193 | + | 17.2599i | 0.730915 | + | 0.666808i | ||||
\(671\) | 7.55586 | 0.291691 | ||||||||
\(672\) | − | 6.75307i | − | 0.260505i | ||||||
\(673\) | − | 45.1688i | − | 1.74113i | −0.492054 | − | 0.870565i | \(-0.663754\pi\) | ||
0.492054 | − | 0.870565i | \(-0.336246\pi\) | |||||||
\(674\) | 16.0649 | 0.618796 | ||||||||
\(675\) | 15.1293 | − | 1.39074i | 0.582326 | − | 0.0535295i | ||||
\(676\) | 11.4014 | 0.438516 | ||||||||
\(677\) | − | 46.9628i | − | 1.80493i | −0.430767 | − | 0.902463i | \(-0.641757\pi\) | ||
0.430767 | − | 0.902463i | \(-0.358243\pi\) | |||||||
\(678\) | 2.21179i | 0.0849432i | ||||||||
\(679\) | 34.0863 | 1.30811 | ||||||||
\(680\) | −24.3022 | − | 22.1707i | −0.931946 | − | 0.850207i | ||||
\(681\) | −8.43871 | −0.323372 | ||||||||
\(682\) | − | 6.04231i | − | 0.231372i | ||||||
\(683\) | − | 19.4215i | − | 0.743142i | −0.928405 | − | 0.371571i | \(-0.878819\pi\) | ||
0.928405 | − | 0.371571i | \(-0.121181\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.56165 | − | 3.90406i | 0.136084 | − | 0.149167i | ||||
\(686\) | 18.6295 | 0.711277 | ||||||||
\(687\) | 6.05137i | 0.230874i | ||||||||
\(688\) | 14.4200i | 0.549758i | ||||||||
\(689\) | 8.34879 | 0.318063 | ||||||||
\(690\) | 3.14660 | − | 3.44911i | 0.119789 | − | 0.131306i | ||||
\(691\) | −17.8669 | −0.679688 | −0.339844 | − | 0.940482i | \(-0.610374\pi\) | ||||
−0.339844 | + | 0.940482i | \(0.610374\pi\) | |||||||
\(692\) | 8.00197i | 0.304189i | ||||||||
\(693\) | 6.20213i | 0.235599i | ||||||||
\(694\) | 0.0866178 | 0.00328797 | ||||||||
\(695\) | −4.03530 | − | 3.68137i | −0.153068 | − | 0.139642i | ||||
\(696\) | 6.42350 | 0.243482 | ||||||||
\(697\) | 25.7254i | 0.974418i | ||||||||
\(698\) | − | 4.86343i | − | 0.184084i | ||||||
\(699\) | −8.43110 | −0.318894 | ||||||||
\(700\) | −12.3199 | + | 1.13249i | −0.465650 | + | 0.0428042i | ||||
\(701\) | 4.30484 | 0.162591 | 0.0812957 | − | 0.996690i | \(-0.474094\pi\) | ||||
0.0812957 | + | 0.996690i | \(0.474094\pi\) | |||||||
\(702\) | 1.94406i | 0.0733739i | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −6.34150 | −0.239004 | ||||||||
\(705\) | −2.98507 | − | 2.72325i | −0.112424 | − | 0.102564i | ||||
\(706\) | 4.18335 | 0.157442 | ||||||||
\(707\) | − | 48.6059i | − | 1.82801i | ||||||
\(708\) | − | 4.80703i | − | 0.180659i | ||||||
\(709\) | −35.1319 | −1.31941 | −0.659703 | − | 0.751526i | \(-0.729318\pi\) | ||||
−0.659703 | + | 0.751526i | \(0.729318\pi\) | |||||||
\(710\) | 1.06977 | − | 1.17262i | 0.0401479 | − | 0.0440077i | ||||
\(711\) | 9.45592 | 0.354625 | ||||||||
\(712\) | 17.9048i | 0.671012i | ||||||||
\(713\) | 25.9818i | 0.973028i | ||||||||
\(714\) | −7.38047 | −0.276207 | ||||||||
\(715\) | 0.766662 | − | 0.840369i | 0.0286715 | − | 0.0314280i | ||||
\(716\) | 4.93502 | 0.184431 | ||||||||
\(717\) | 11.0887i | 0.414114i | ||||||||
\(718\) | 31.6523i | 1.18125i | ||||||||
\(719\) | −29.4030 | −1.09655 | −0.548273 | − | 0.836299i | \(-0.684715\pi\) | ||||
−0.548273 | + | 0.836299i | \(0.684715\pi\) | |||||||
\(720\) | −6.18965 | − | 5.64677i | −0.230675 | − | 0.210443i | ||||
\(721\) | −14.3004 | −0.532574 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.1087i | 0.561898i | ||||||||
\(724\) | −16.9902 | −0.631437 | ||||||||
\(725\) | −1.81938 | − | 19.7923i | −0.0675702 | − | 0.735069i | ||||
\(726\) | 5.73700 | 0.212920 | ||||||||
\(727\) | − | 22.5569i | − | 0.836589i | −0.908312 | − | 0.418294i | \(-0.862628\pi\) | ||
0.908312 | − | 0.418294i | \(-0.137372\pi\) | |||||||
\(728\) | − | 5.08952i | − | 0.188630i | ||||||
\(729\) | 12.9222 | 0.478599 | ||||||||
\(730\) | 12.1348 | + | 11.0705i | 0.449130 | + | 0.409738i | ||||
\(731\) | −50.6023 | −1.87159 | ||||||||
\(732\) | − | 4.35364i | − | 0.160915i | ||||||
\(733\) | 37.9002i | 1.39988i | 0.714204 | + | 0.699938i | \(0.246789\pi\) | ||||
−0.714204 | + | 0.699938i | \(0.753211\pi\) | |||||||
\(734\) | −18.9998 | −0.701295 | ||||||||
\(735\) | −0.407994 | + | 0.447218i | −0.0150491 | + | 0.0164959i | ||||
\(736\) | 17.3929 | 0.641113 | ||||||||
\(737\) | 9.10669i | 0.335449i | ||||||||
\(738\) | 15.1339i | 0.557087i | ||||||||
\(739\) | 26.0215 | 0.957218 | 0.478609 | − | 0.878028i | \(-0.341141\pi\) | ||||
0.478609 | + | 0.878028i | \(0.341141\pi\) | |||||||
\(740\) | −5.89312 | + | 6.45968i | −0.216635 | + | 0.237463i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 39.2300i | 1.44018i | ||||||||
\(743\) | − | 50.3874i | − | 1.84854i | −0.381744 | − | 0.924268i | \(-0.624677\pi\) | ||
0.381744 | − | 0.924268i | \(-0.375323\pi\) | |||||||
\(744\) | −11.1930 | −0.410357 | ||||||||
\(745\) | −23.5707 | − | 21.5034i | −0.863565 | − | 0.787824i | ||||
\(746\) | 26.4103 | 0.966951 | ||||||||
\(747\) | − | 13.5194i | − | 0.494650i | ||||||
\(748\) | − | 3.63852i | − | 0.133037i | ||||||
\(749\) | 41.6177 | 1.52068 | ||||||||
\(750\) | 3.75595 | − | 4.96232i | 0.137148 | − | 0.181198i | ||||
\(751\) | −27.1857 | −0.992021 | −0.496011 | − | 0.868316i | \(-0.665202\pi\) | ||||
−0.496011 | + | 0.868316i | \(0.665202\pi\) | |||||||
\(752\) | 4.68811i | 0.170958i | ||||||||
\(753\) | − | 13.1873i | − | 0.480570i | ||||||
\(754\) | 2.54325 | 0.0926197 | ||||||||
\(755\) | −3.87077 | − | 3.53128i | −0.140872 | − | 0.128516i | ||||
\(756\) | 7.51867 | 0.273451 | ||||||||
\(757\) | − | 32.8983i | − | 1.19571i | −0.801605 | − | 0.597855i | \(-0.796020\pi\) | ||
0.801605 | − | 0.597855i | \(-0.203980\pi\) | |||||||
\(758\) | 28.8700i | 1.04860i | ||||||||
\(759\) | 1.66021 | 0.0602619 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.47213 | 0.125865 | 0.0629323 | − | 0.998018i | \(-0.479955\pi\) | ||||
0.0629323 | + | 0.998018i | \(0.479955\pi\) | |||||||
\(762\) | − | 5.11277i | − | 0.185216i | ||||||
\(763\) | 10.7491i | 0.389145i | ||||||||
\(764\) | −15.5854 | −0.563859 | ||||||||
\(765\) | 19.8155 | − | 21.7206i | 0.716431 | − | 0.785308i | ||||
\(766\) | −19.1923 | −0.693445 | ||||||||
\(767\) | − | 6.11886i | − | 0.220939i | ||||||
\(768\) | 8.81622i | 0.318128i | ||||||||
\(769\) | 31.6735 | 1.14218 | 0.571089 | − | 0.820888i | \(-0.306521\pi\) | ||||
0.571089 | + | 0.820888i | \(0.306521\pi\) | |||||||
\(770\) | 3.94880 | + | 3.60246i | 0.142305 | + | 0.129824i | ||||
\(771\) | −2.89229 | −0.104163 | ||||||||
\(772\) | − | 6.74883i | − | 0.242896i | ||||||
\(773\) | 35.0686i | 1.26133i | 0.776056 | + | 0.630665i | \(0.217218\pi\) | ||||
−0.776056 | + | 0.630665i | \(0.782782\pi\) | |||||||
\(774\) | −29.7687 | −1.07001 | ||||||||
\(775\) | 3.17030 | + | 34.4884i | 0.113881 | + | 1.23886i | ||||
\(776\) | −37.8207 | −1.35768 | ||||||||
\(777\) | 6.30706i | 0.226265i | ||||||||
\(778\) | − | 7.52562i | − | 0.269807i | ||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −0.484215 | − | 0.441746i | −0.0173377 | − | 0.0158170i | ||||
\(781\) | 0.564435 | 0.0201971 | ||||||||
\(782\) | − | 19.0089i | − | 0.679755i | ||||||
\(783\) | 12.0790i | 0.431667i | ||||||||
\(784\) | 0.702366 | 0.0250845 | ||||||||
\(785\) | −24.3759 | + | 26.7194i | −0.870014 | + | 0.953656i | ||||
\(786\) | 2.08132 | 0.0742383 | ||||||||
\(787\) | 42.1829i | 1.50366i | 0.659358 | + | 0.751829i | \(0.270828\pi\) | ||||
−0.659358 | + | 0.751829i | \(0.729172\pi\) | |||||||
\(788\) | − | 11.0232i | − | 0.392685i | ||||||
\(789\) | −10.3738 | −0.369316 | ||||||||
\(790\) | 5.49240 | − | 6.02044i | 0.195411 | − | 0.214198i | ||||
\(791\) | 10.8885 | 0.387150 | ||||||||
\(792\) | − | 6.88162i | − | 0.244528i | ||||||
\(793\) | − | 5.54174i | − | 0.196793i | ||||||
\(794\) | 12.2800 | 0.435801 | ||||||||
\(795\) | 11.9993 | + | 10.9469i | 0.425572 | + | 0.388246i | ||||
\(796\) | 7.00496 | 0.248284 | ||||||||
\(797\) | − | 20.4194i | − | 0.723291i | −0.932316 | − | 0.361646i | \(-0.882215\pi\) | ||
0.932316 | − | 0.361646i | \(-0.117785\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.4514 | −0.582008 | ||||||||
\(800\) | 23.0875 | − | 2.12228i | 0.816265 | − | 0.0750341i | ||||
\(801\) | −16.0028 | −0.565432 | ||||||||
\(802\) | 41.0711i | 1.45027i | ||||||||
\(803\) | 5.84103i | 0.206125i | ||||||||
\(804\) | 5.24722 | 0.185055 | ||||||||
\(805\) | −16.9798 | − | 15.4905i | −0.598458 | − | 0.545969i | ||||
\(806\) | −4.43165 | −0.156098 | ||||||||
\(807\) | − | 9.87696i | − | 0.347685i | ||||||
\(808\) | 53.9310i | 1.89729i | ||||||||
\(809\) | −28.5536 | −1.00389 | −0.501946 | − | 0.864899i | \(-0.667382\pi\) | ||||
−0.501946 | + | 0.864899i | \(0.667382\pi\) | |||||||
\(810\) | 10.3197 | − | 11.3119i | 0.362598 | − | 0.397458i | ||||
\(811\) | 1.61158 | 0.0565904 | 0.0282952 | − | 0.999600i | \(-0.490992\pi\) | ||||
0.0282952 | + | 0.999600i | \(0.490992\pi\) | |||||||
\(812\) | − | 9.83603i | − | 0.345177i | ||||||
\(813\) | − | 1.00558i | − | 0.0352673i | ||||||
\(814\) | 3.77774 | 0.132410 | ||||||||
\(815\) | 24.1514 | − | 26.4733i | 0.845987 | − | 0.927320i | ||||
\(816\) | 3.54540 | 0.124114 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | − | 9.29706i | − | 0.325064i | ||||||
\(819\) | 4.54886 | 0.158950 | ||||||||
\(820\) | −7.93069 | − | 7.23511i | −0.276952 | − | 0.252661i | ||||
\(821\) | −8.04886 | −0.280907 | −0.140454 | − | 0.990087i | \(-0.544856\pi\) | ||||
−0.140454 | + | 0.990087i | \(0.544856\pi\) | |||||||
\(822\) | 1.31555i | 0.0458849i | ||||||||
\(823\) | − | 37.3423i | − | 1.30167i | −0.759219 | − | 0.650835i | \(-0.774419\pi\) | ||
0.759219 | − | 0.650835i | \(-0.225581\pi\) | |||||||
\(824\) | 15.8671 | 0.552757 | ||||||||
\(825\) | 2.20377 | − | 0.202579i | 0.0767255 | − | 0.00705289i | ||||
\(826\) | 28.7518 | 1.00040 | ||||||||
\(827\) | − | 10.9302i | − | 0.380082i | −0.981776 | − | 0.190041i | \(-0.939138\pi\) | ||
0.981776 | − | 0.190041i | \(-0.0608620\pi\) | |||||||
\(828\) | 9.20409i | 0.319864i | ||||||||
\(829\) | 33.6375 | 1.16828 | 0.584139 | − | 0.811654i | \(-0.301432\pi\) | ||||
0.584139 | + | 0.811654i | \(0.301432\pi\) | |||||||
\(830\) | −8.60761 | − | 7.85266i | −0.298775 | − | 0.272570i | ||||
\(831\) | 3.60265 | 0.124975 | ||||||||
\(832\) | 4.65108i | 0.161247i | ||||||||
\(833\) | 2.46472i | 0.0853976i | ||||||||
\(834\) | 1.35977 | 0.0470849 | ||||||||
\(835\) | −11.4180 | + | 12.5157i | −0.395136 | + | 0.433124i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 21.0478i | − | 0.727517i | ||||||
\(838\) | − | 8.17179i | − | 0.282290i | ||||||
\(839\) | 13.8735 | 0.478965 | 0.239483 | − | 0.970901i | \(-0.423022\pi\) | ||||
0.239483 | + | 0.970901i | \(0.423022\pi\) | |||||||
\(840\) | 6.67335 | − | 7.31493i | 0.230253 | − | 0.252389i | ||||
\(841\) | −13.1981 | −0.455108 | ||||||||
\(842\) | 36.1951i | 1.24737i | ||||||||
\(843\) | − | 6.52948i | − | 0.224887i | ||||||
\(844\) | −9.08103 | −0.312582 | ||||||||
\(845\) | 20.8586 | + | 19.0292i | 0.717558 | + | 0.654623i | ||||
\(846\) | −9.67815 | −0.332741 | ||||||||
\(847\) | − | 28.2429i | − | 0.970437i | ||||||
\(848\) | − | 18.8452i | − | 0.647146i | ||||||
\(849\) | 13.6406 | 0.468145 | ||||||||
\(850\) | −2.31946 | − | 25.2324i | −0.0795567 | − | 0.865466i | ||||
\(851\) | −16.2442 | −0.556845 | ||||||||
\(852\) | − | 0.325224i | − | 0.0111420i | ||||||
\(853\) | − | 29.5477i | − | 1.01169i | −0.862624 | − | 0.505846i | \(-0.831180\pi\) | ||
0.862624 | − | 0.505846i | \(-0.168820\pi\) | |||||||
\(854\) | 26.0400 | 0.891071 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −46.1773 | −1.57831 | ||||||||
\(857\) | 4.28588i | 0.146403i | 0.997317 | + | 0.0732014i | \(0.0233216\pi\) | ||||
−0.997317 | + | 0.0732014i | \(0.976678\pi\) | |||||||
\(858\) | 0.283178i | 0.00966753i | ||||||||
\(859\) | 34.9764 | 1.19338 | 0.596689 | − | 0.802472i | \(-0.296483\pi\) | ||||
0.596689 | + | 0.802472i | \(0.296483\pi\) | |||||||
\(860\) | 14.2316 | − | 15.5998i | 0.485294 | − | 0.531950i | ||||
\(861\) | −7.74331 | −0.263891 | ||||||||
\(862\) | 2.97412i | 0.101299i | ||||||||
\(863\) | − | 20.0305i | − | 0.681848i | −0.940091 | − | 0.340924i | \(-0.889260\pi\) | ||
0.940091 | − | 0.340924i | \(-0.110740\pi\) | |||||||
\(864\) | −14.0899 | −0.479349 | ||||||||
\(865\) | −13.3554 | + | 14.6394i | −0.454098 | + | 0.497755i | ||||
\(866\) | 22.8886 | 0.777786 | ||||||||
\(867\) | 3.40674i | 0.115699i | ||||||||
\(868\) | 17.1394i | 0.581750i | ||||||||
\(869\) | 2.89791 | 0.0983047 | ||||||||
\(870\) | 3.65529 | + | 3.33470i | 0.123926 | + | 0.113057i | ||||
\(871\) | 6.67917 | 0.226315 | ||||||||
\(872\) | − | 11.9268i | − | 0.403892i | ||||||
\(873\) | − | 33.8030i | − | 1.14406i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −24.4292 | − | 18.4903i | −0.825857 | − | 0.625087i | ||||
\(876\) | 3.36556 | 0.113712 | ||||||||
\(877\) | 45.5920i | 1.53953i | 0.638326 | + | 0.769766i | \(0.279627\pi\) | ||||
−0.638326 | + | 0.769766i | \(0.720373\pi\) | |||||||
\(878\) | − | 34.1202i | − | 1.15150i | ||||||
\(879\) | 14.9402 | 0.503922 | ||||||||
\(880\) | −1.89691 | − | 1.73054i | −0.0639448 | − | 0.0583364i | ||||
\(881\) | −17.2730 | −0.581941 | −0.290971 | − | 0.956732i | \(-0.593978\pi\) | ||||
−0.290971 | + | 0.956732i | \(0.593978\pi\) | |||||||
\(882\) | 1.44997i | 0.0488229i | ||||||||
\(883\) | − | 35.1932i | − | 1.18434i | −0.805812 | − | 0.592172i | \(-0.798271\pi\) | ||
0.805812 | − | 0.592172i | \(-0.201729\pi\) | |||||||
\(884\) | −2.66862 | −0.0897554 | ||||||||
\(885\) | 8.02301 | − | 8.79434i | 0.269691 | − | 0.295619i | ||||
\(886\) | 8.12966 | 0.273121 | ||||||||
\(887\) | 3.16110i | 0.106139i | 0.998591 | + | 0.0530697i | \(0.0169005\pi\) | ||||
−0.998591 | + | 0.0530697i | \(0.983099\pi\) | |||||||
\(888\) | − | 6.99805i | − | 0.234839i | ||||||
\(889\) | −25.1698 | −0.844169 | ||||||||
\(890\) | −9.29512 | + | 10.1887i | −0.311573 | + | 0.341528i | ||||
\(891\) | 5.44491 | 0.182411 | ||||||||
\(892\) | − | 25.5727i | − | 0.856237i | ||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 7.94259 | 0.265640 | ||||||||
\(895\) | 9.02851 | + | 8.23664i | 0.301790 | + | 0.275321i | ||||
\(896\) | 3.55870 | 0.118888 | ||||||||
\(897\) | − | 1.21766i | − | 0.0406565i | ||||||
\(898\) | − | 24.0715i | − | 0.803277i | ||||||
\(899\) | −27.5350 | −0.918343 | ||||||||
\(900\) | 1.12308 | + | 12.2176i | 0.0374361 | + | 0.407252i | ||||
\(901\) | 66.1310 | 2.20314 | ||||||||
\(902\) | 4.63801i | 0.154429i | ||||||||
\(903\) | − | 15.2312i | − | 0.506864i | ||||||
\(904\) | −12.0814 | −0.401822 | ||||||||
\(905\) | −31.0832 | − | 28.3570i | −1.03324 | − | 0.942619i | ||||
\(906\) | 1.30433 | 0.0433334 | ||||||||
\(907\) | − | 15.9313i | − | 0.528991i | −0.964387 | − | 0.264495i | \(-0.914795\pi\) | ||
0.964387 | − | 0.264495i | \(-0.0852054\pi\) | |||||||
\(908\) | − | 14.3375i | − | 0.475807i | ||||||
\(909\) | −48.2019 | −1.59876 | ||||||||
\(910\) | 2.64217 | − | 2.89619i | 0.0875872 | − | 0.0960078i | ||||
\(911\) | −0.0577380 | −0.00191294 | −0.000956472 | − | 1.00000i | \(-0.500304\pi\) | ||||
−0.000956472 | 1.00000i | \(0.500304\pi\) | ||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 4.14323i | − | 0.137121i | ||||||
\(914\) | −3.54929 | −0.117400 | ||||||||
\(915\) | 7.26630 | − | 7.96488i | 0.240216 | − | 0.263311i | ||||
\(916\) | −10.2814 | −0.339706 | ||||||||
\(917\) | − | 10.2462i | − | 0.338360i | ||||||
\(918\) | 15.3990i | 0.508242i | ||||||||
\(919\) | −50.0489 | −1.65096 | −0.825481 | − | 0.564430i | \(-0.809096\pi\) | ||||
−0.825481 | + | 0.564430i | \(0.809096\pi\) | |||||||
\(920\) | 18.8400 | + | 17.1876i | 0.621138 | + | 0.566659i | ||||
\(921\) | −1.36943 | −0.0451242 | ||||||||
\(922\) | 11.3674i | 0.374365i | ||||||||
\(923\) | − | 0.413977i | − | 0.0136262i | ||||||
\(924\) | 1.09519 | 0.0360291 | ||||||||
\(925\) | −21.5626 | + | 1.98212i | −0.708975 | + | 0.0651716i | ||||
\(926\) | 7.65831 | 0.251668 | ||||||||
\(927\) | 14.1816i | 0.465783i | ||||||||
\(928\) | 18.4327i | 0.605081i | ||||||||
\(929\) | 16.9850 | 0.557259 | 0.278629 | − | 0.960399i | \(-0.410120\pi\) | ||||
0.278629 | + | 0.960399i | \(0.410120\pi\) | |||||||
\(930\) | −6.36940 | − | 5.81075i | −0.208861 | − | 0.190542i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 14.3246i | − | 0.469218i | ||||||
\(933\) | − | 7.77874i | − | 0.254665i | ||||||
\(934\) | 11.3557 | 0.371571 | ||||||||
\(935\) | 6.07275 | − | 6.65658i | 0.198600 | − | 0.217694i | ||||
\(936\) | −5.04723 | −0.164974 | ||||||||
\(937\) | 33.6925i | 1.10069i | 0.834938 | + | 0.550344i | \(0.185503\pi\) | ||||
−0.834938 | + | 0.550344i | \(0.814497\pi\) | |||||||
\(938\) | 31.3847i | 1.02475i | ||||||||
\(939\) | 0.794036 | 0.0259124 | ||||||||
\(940\) | 4.62685 | − | 5.07168i | 0.150911 | − | 0.165420i | ||||
\(941\) | 27.1733 | 0.885823 | 0.442911 | − | 0.896565i | \(-0.353946\pi\) | ||||
0.442911 | + | 0.896565i | \(0.353946\pi\) | |||||||
\(942\) | − | 9.00360i | − | 0.293353i | ||||||
\(943\) | − | 19.9434i | − | 0.649446i | ||||||
\(944\) | −13.8117 | −0.449532 | ||||||||
\(945\) | 13.7552 | + | 12.5488i | 0.447458 | + | 0.408212i | ||||
\(946\) | −9.12306 | −0.296616 | ||||||||
\(947\) | 33.2962i | 1.08198i | 0.841028 | + | 0.540991i | \(0.181951\pi\) | ||||
−0.841028 | + | 0.540991i | \(0.818049\pi\) | |||||||
\(948\) | − | 1.66975i | − | 0.0542311i | ||||||
\(949\) | 4.28402 | 0.139065 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.99864 | 0.0972376 | ||||||||
\(952\) | − | 40.3142i | − | 1.30659i | ||||||
\(953\) | 30.4086i | 0.985030i | 0.870304 | + | 0.492515i | \(0.163922\pi\) | ||||
−0.870304 | + | 0.492515i | \(0.836078\pi\) | |||||||
\(954\) | 38.9040 | 1.25956 | ||||||||
\(955\) | −28.5131 | − | 26.0123i | −0.922662 | − | 0.841737i | ||||
\(956\) | −18.8399 | −0.609325 | ||||||||
\(957\) | 1.75946i | 0.0568751i | ||||||||
\(958\) | 3.61079i | 0.116659i | ||||||||
\(959\) | 6.47635 | 0.209132 | ||||||||
\(960\) | −6.09847 | + | 6.68478i | −0.196827 | + | 0.215750i | ||||
\(961\) | 16.9801 | 0.547744 | ||||||||
\(962\) | − | 2.77073i | − | 0.0893319i | ||||||
\(963\) | − | 41.2719i | − | 1.32997i | ||||||
\(964\) | −25.6699 | −0.826772 | ||||||||
\(965\) | 11.2639 | − | 12.3468i | 0.362598 | − | 0.397459i | ||||
\(966\) | 5.72165 | 0.184091 | ||||||||
\(967\) | 58.9180i | 1.89467i | 0.320239 | + | 0.947337i | \(0.396237\pi\) | ||||
−0.320239 | + | 0.947337i | \(0.603763\pi\) | |||||||
\(968\) | 31.3371i | 1.00721i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −21.5219 | − | 19.6342i | −0.691025 | − | 0.630417i | ||||
\(971\) | 40.8679 | 1.31151 | 0.655757 | − | 0.754972i | \(-0.272349\pi\) | ||||
0.655757 | + | 0.754972i | \(0.272349\pi\) | |||||||
\(972\) | − | 11.3684i | − | 0.364643i | ||||||
\(973\) | − | 6.69405i | − | 0.214601i | ||||||
\(974\) | 28.2769 | 0.906051 | ||||||||
\(975\) | −0.148579 | − | 1.61633i | −0.00475832 | − | 0.0517639i | ||||
\(976\) | −12.5090 | −0.400403 | ||||||||
\(977\) | − | 35.9431i | − | 1.14992i | −0.818181 | − | 0.574961i | \(-0.805017\pi\) | ||
0.818181 | − | 0.574961i | \(-0.194983\pi\) | |||||||
\(978\) | 8.92068i | 0.285252i | ||||||||
\(979\) | −4.90430 | −0.156742 | ||||||||
\(980\) | −0.759832 | − | 0.693189i | −0.0242719 | − | 0.0221431i | ||||
\(981\) | 10.6598 | 0.340342 | ||||||||
\(982\) | − | 0.255544i | − | 0.00815474i | ||||||
\(983\) | 10.0666i | 0.321074i | 0.987030 | + | 0.160537i | \(0.0513226\pi\) | ||||
−0.987030 | + | 0.160537i | \(0.948677\pi\) | |||||||
\(984\) | 8.59165 | 0.273892 | ||||||||
\(985\) | 18.3979 | − | 20.1667i | 0.586205 | − | 0.642563i | ||||
\(986\) | 20.1452 | 0.641553 | ||||||||
\(987\) | − | 4.95185i | − | 0.157619i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 39.2290 | 1.24741 | ||||||||
\(990\) | 3.57252 | − | 3.91598i | 0.113542 | − | 0.124458i | ||||
\(991\) | 18.0301 | 0.572745 | 0.286372 | − | 0.958118i | \(-0.407551\pi\) | ||||
0.286372 | + | 0.958118i | \(0.407551\pi\) | |||||||
\(992\) | − | 32.1191i | − | 1.01978i | ||||||
\(993\) | 16.9491i | 0.537864i | ||||||||
\(994\) | 1.94523 | 0.0616989 | ||||||||
\(995\) | 12.8154 | + | 11.6914i | 0.406276 | + | 0.370642i | ||||
\(996\) | −2.38730 | −0.0756446 | ||||||||
\(997\) | − | 18.7246i | − | 0.593014i | −0.955031 | − | 0.296507i | \(-0.904178\pi\) | ||
0.955031 | − | 0.296507i | \(-0.0958218\pi\) | |||||||
\(998\) | − | 3.40268i | − | 0.107710i | ||||||
\(999\) | 13.1594 | 0.416344 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1805.2.b.l.1084.9 | 24 | ||
5.2 | odd | 4 | 9025.2.a.ct.1.16 | 24 | |||
5.3 | odd | 4 | 9025.2.a.ct.1.9 | 24 | |||
5.4 | even | 2 | inner | 1805.2.b.l.1084.16 | 24 | ||
19.2 | odd | 18 | 95.2.p.a.4.6 | yes | 48 | ||
19.10 | odd | 18 | 95.2.p.a.24.3 | yes | 48 | ||
19.18 | odd | 2 | 1805.2.b.k.1084.16 | 24 | |||
57.2 | even | 18 | 855.2.da.b.289.3 | 48 | |||
57.29 | even | 18 | 855.2.da.b.784.6 | 48 | |||
95.2 | even | 36 | 475.2.l.f.251.6 | 48 | |||
95.18 | even | 4 | 9025.2.a.cu.1.16 | 24 | |||
95.29 | odd | 18 | 95.2.p.a.24.6 | yes | 48 | ||
95.37 | even | 4 | 9025.2.a.cu.1.9 | 24 | |||
95.48 | even | 36 | 475.2.l.f.176.3 | 48 | |||
95.59 | odd | 18 | 95.2.p.a.4.3 | ✓ | 48 | ||
95.67 | even | 36 | 475.2.l.f.176.6 | 48 | |||
95.78 | even | 36 | 475.2.l.f.251.3 | 48 | |||
95.94 | odd | 2 | 1805.2.b.k.1084.9 | 24 | |||
285.29 | even | 18 | 855.2.da.b.784.3 | 48 | |||
285.59 | even | 18 | 855.2.da.b.289.6 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.p.a.4.3 | ✓ | 48 | 95.59 | odd | 18 | ||
95.2.p.a.4.6 | yes | 48 | 19.2 | odd | 18 | ||
95.2.p.a.24.3 | yes | 48 | 19.10 | odd | 18 | ||
95.2.p.a.24.6 | yes | 48 | 95.29 | odd | 18 | ||
475.2.l.f.176.3 | 48 | 95.48 | even | 36 | |||
475.2.l.f.176.6 | 48 | 95.67 | even | 36 | |||
475.2.l.f.251.3 | 48 | 95.78 | even | 36 | |||
475.2.l.f.251.6 | 48 | 95.2 | even | 36 | |||
855.2.da.b.289.3 | 48 | 57.2 | even | 18 | |||
855.2.da.b.289.6 | 48 | 285.59 | even | 18 | |||
855.2.da.b.784.3 | 48 | 285.29 | even | 18 | |||
855.2.da.b.784.6 | 48 | 57.29 | even | 18 | |||
1805.2.b.k.1084.9 | 24 | 95.94 | odd | 2 | |||
1805.2.b.k.1084.16 | 24 | 19.18 | odd | 2 | |||
1805.2.b.l.1084.9 | 24 | 1.1 | even | 1 | trivial | ||
1805.2.b.l.1084.16 | 24 | 5.4 | even | 2 | inner | ||
9025.2.a.ct.1.9 | 24 | 5.3 | odd | 4 | |||
9025.2.a.ct.1.16 | 24 | 5.2 | odd | 4 | |||
9025.2.a.cu.1.9 | 24 | 95.37 | even | 4 | |||
9025.2.a.cu.1.16 | 24 | 95.18 | even | 4 |